Slippery rough surfaces

ABSTRACT

Substrates having a textured surface that can maintain or improve droplet mobility in both the Cassie and Wenzel states include a textured surface and a conformal lubricant layer thereover. The textured surface can include a plurality of raised first elements and a plurality of second elements thereon and the conformal lubricant layer over the plurality of raised first elements and covering the plurality of second elements. The plurality of raised first elements can have an average height of between 0.5 μm and 500 μm, and the plurality of second elements can have an average height of between 0.01 μm and 10 μm. Such substrates can be prepared by texturing a surface of a substrate with a plurality of raised first elements and a plurality of second elements thereon; optionally silanizing the textured surface and applying a lubricant layer over the plurality of raised first elements and between the plurality of second elements.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.62/152,532 filed Apr. 24, 2015, the entire disclosure of which is herebyincorporated by reference herein.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under Contract No.N00014-12-1-0962, awarded by the Office of Naval Research, underContract No. CMMI1351462 awarded by the National Science Foundation, NSFGraduate Research Fellowship (Grant No. DGE1255832), and under Grant No.DE-AR0000326, awarded by the Department of Energy. The Government hascertain rights in the invention.

TECHNICAL FIELD

The present disclosure relates to substrates having a textured surfaceand a conformal lubricant layer thereover which can be used for fogharvesting, dropwise condensation, oil adsorption, oil/water separation,drag reduction, anti-fouling and anti-biofouling, anti-frosting andanti-icing devices and applications.

BACKGROUND

Enhancing the mobility of liquid droplets on rough surfaces is of greatinterest in industry. Applications range from condensation heat transferto water harvesting to the prevention of icing and frosting. Themobility of a liquid droplet on a rough solid surface has long beenassociated with its wetting state. When liquid drops are sitting on thetips of solid textures and air is trapped underneath, they are in theCassie state. When the drops are impregnated within the solid textures,they are in the Wenzel state. The Cassie state has been associated withhigh droplet mobility, while the Wenzel state has been associated withdroplet pinning.

Many plants, insects, and animals have highly liquid repellent surfaces,with well-known examples including lotus leaves, the legs of waterstriders, and the feet of tokay geckos. The liquid repellent function ofthese natural surfaces is attributed to the presence of hydrophobichierarchical micro- and nanoscale surface textures that maintain liquiddroplets in the Cassie state. Surface textures yielding Cassie statedroplets are surfaces with superhydrophobic or superomniphobicproperties, with a typical liquid contact angle over 150° and contactangle hysteresis less than 10°. Liquids on these surfaces can roll offwith minimal tilting owing to the reduced liquid-solid contact area.Inspired by these natural surfaces, a range of engineeredsuperhydrophobic or superomniphobic surfaces have been developed overthe last decade with technological applications ranging fromself-cleaning surfaces to drag reduction coatings.

Liquid droplets on rough surfaces typically exhibit Cassie state, Wenzelstate, or a combination of these two states. It is often desirable tomaintain high liquid repellency in industrial applications, such as fogharvesting, dropwise condensation, and anti-icing. Because theconventional Wenzel state has long been associated with droplet pinning,intense research has focused on maintaining liquid droplets in theCassie state. Sustaining a droplet in this state is difficult undercertain conditions, however, as the air layer underneath the dropletscan be disrupted when subjected to high pressure or high temperature, orwhen encountering liquids with impurities or low surface tensions. Oncethe air layer is depleted, the liquid will impregnate the solidtextures. As a result, the liquid strongly adheres to the solid surfacedue to the increased contact area of the liquid-solid interfaces andliquid pinning at defects in the solid substrate.

Once a droplet is in the conventional Wenzel state on a roughenedsurface, it becomes immobile. In an effort to recover droplet mobility,previous researches have been predominantly focused on the ways toinduce Wenzel-to-Cassie transition. Thus far, very few design strategiescan restore the liquid from the fully impregnated Wenzel state to theCassie state, and strategies successful in doing so require the use ofexternal energy.

Several publications disclose slippery liquid-infused porous surfaces(SLIPS) to repel liquids. See, e.g., WO2012100099, WO2012100100,WO2013115868 to Aizenberg et al. Other publications disclose methods andcompositions related to liquid repellant surfaces having selectivewetting and transport properties. See, e.g., WO2014012078, WO2014012079to Aizenberg et al. Additional references disclose liquid-impregnatedsurfaces with non-wetting properties. See, e.g., WO2013022467,WO2014145414 to Smith et al. and Kim et al., Hierarchical or Not? Effectof the length Scale and Hierarchy of the Surface Roughness onOmnbiphobicity of Lubricant-infused Substrates, Nano Letters,2013:13:1793-99.

However, there is a continuing need for technology that provides asimple solution to maintain droplet mobility without requiringchallenging transitions, and for new liquid-repellent surface designs.

SUMMARY OF THE DISCLOSURE

An advantage of the present disclosure is a surface design that canmaintain droplet mobility in both the Cassie and Wenzel states. Suchslippery rough surfaces advantageously have a high surface area andslippery interface and can be used in fog harvesting, dropwisecondensation, oil adsorption, oil/water separation, drag reduction,anti-fouling and anti-biofouling, and anti-icing/frosting devices andapplications.

These and other advantages are satisfied, at least in part, by atextured surface that can maintain droplet mobility in both the Cassieand Wenzel states. The textured surface can include a plurality ofraised first elements and a plurality of second elements thereon and aconformal lubricant layer over the plurality of raised first elementsand covering the plurality of second elements. Advantageously, theconformal lubricant layer can have a uniform thickness over theplurality of raised first elements since the thickness is governed bythe height of the second elements.

In some embodiments, the plurality of raised first elements can have anaverage height of between 0.5 μm and 500 μm, and the plurality of secondelements can have an average height of between 0.01 μm and 10 μm. Inother embodiments, the substrate can include a silanized coating betweenthe conformal lubricant layer and either the plurality of raised firstelements or the plurality of second elements or both. In still furtherembodiments, the lubricant can be one or more of an oleophobiclubricant, an oleophilic lubricant, a hydrophobic lubricant and/or ahydrophilic lubricant.

Another aspect of the present disclosure includes a method of preparinga slippery rough surface. The method comprises texturing a surface of asubstrate with a plurality of raised first elements and a plurality ofsecond elements thereon; and applying a lubricant layer over theplurality of raised first elements and between the plurality of secondelements. Advantageously, the lubricant layer can be applied to form aconformal lubricant layer over the plurality of raised first elements.The method can advantageously be applied to surfaces of the substratesthat are metals, plastics, ceramics, glass or combinations thereof. Insome embodiments, the method includes silanizing the textured surfaceprior to applying the lubricant layer.

Additional advantages of the present invention will become readilyapparent to those skilled in this art from the following detaileddescription, wherein only the preferred embodiment of the invention isshown and described, simply by way of illustration of the best modecontemplated of carrying out the invention. As will be realized, theinvention is capable of other and different embodiments, and its severaldetails are capable of modifications in various obvious respects, allwithout departing from the invention. Accordingly, the drawings anddescription are to be regarded as illustrative in nature, and not asrestrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference is made to the attached drawings, wherein elements having thesame reference numeral designations represent similar elementsthroughout and wherein:

FIGS. 1a-1e illustrate the fabrication of a slippery rough surface anddroplets in a Cassie and Wenzel state on such a surface. For example,FIGS. 1a-c show a method including texturing a surface of a substratewith a plurality of raised first elements and a plurality of secondelements thereon; silanizing the textured surface; and applying alubricant layer over the plurality of raised first elements and fullycovering the plurality of second elements. FIG. 1d shows a Cassie statedroplet on a slippery rough surfaces (w=50 μm, L=50 μm, h=50 μm)according to an embodiment of the present disclosure. The bright areabetween the droplet and solid surface indicates the existence of a gaslayer, e.g., air. The sliding angle is 8°. FIG. 1e shows a Wenzel statedroplet on the slippery rough surface (w=47 μm, L=53 μm, h=19 μm)according to an embodiment of the present disclosure with the slidingangle of 18°. No gas layer exists between the water droplet and solidsurface. The drop volumes are 10 μL and all images share the same scalebar.

FIGS. 2a-2f are characterizations of surface retention force of waterdroplets on lubricated and non-lubricated rough surfaces. Note thatlubricated rough surface is equivalent to slippery rough surface. FIG.2a shows an SEM image of a silicon micropillar; FIG. 2b shows an SEMimage of a nanotextured micropillar. Nanostructures were formed at thetop and side walls of the micropillar and the bottom of the substrate bya wet etching process. FIG. 2c shows an ESEM image of a lubricatedmicropillar. The lubricant (Krytox 101) was retained within thenanotextures and the lubricated micropillars exhibit flat surfacetopography similar to that of the silanized micropillar withoutnanotextures. FIG. 2d is a cross section of bare micropillars, and FIG.2e is a cross section of lubricated micropillars (w=47 μm, L=53 μm, h=19μm; solid fraction=0.22). FIG. 2f is a chart plotting the retentionforce F of liquid droplets on lubricated rough surfaces over surfaceroughness R (R is defined as the ratio of the actual surface area of theelements and the projected area). The coefficient of determination is0.996 for the linear fit curve depicted here. Error bars indicatestandard deviations from three independent measurements.

FIG. 3 shows experimentally measured apparent contact angles of variousliquid droplets in the Wenzel state as a function of surface roughnessof the slippery rough surfaces. It illustrates the wettingcharacteristics of the slippery rough surfaces. Experimental dataincludes the apparent static, advancing, and receding angles ofdifferent liquids. Error bars represent the standard deviation of atleast three data points. Because slippery rough surfaces allow forWenzel state droplet mobility, and thus lower contact angle hysteresiscompared to conventional Wenzel state droplets, we can measure theapparent contact angle with higher accuracy. More accurate experimentalmeasurements allow for more accurate verification of equationspredicting apparent contact angle.

FIGS. 4a-4e show aqueous and organic liquid droplets in the Wenzel stateon lubricated and non-lubricated rough surfaces. Note that lubricatedrough surface is equivalent to slippery rough surface. FIG. 4a isschematic of a drop with low surface tension in Wenzel state on alubricated rough surface, showing a low contact angle. FIG. 4b shows a10 μL droplet of hexadecane on the lubricated rough surfaces, displayinga sliding angle of 15°. FIG. 4c is a schematic of a drop with lowsurface tension on silanized micropillars, showing a low contact anglein Wenzel state. FIG. 4d shows a 10 μL droplet of hexadecane onmicrostructured surfaces with a tilt angle of 90°. The drop is stronglypinned on the surface, exhibiting the sticky Wenzel state. FIG. 4e shownormalized retention force F* of liquids with different surface tensionson lubricated rough surfaces. The value for F* was defined as the ratioof the retention force on the lubricated surfaces to that of thenon-lubricated surfaces. Here, R=1.36. The micropillar dimension in thisfigure is: w=47 μm, L=53 μm, h=19 μm. FIGS. 4b and 4d share the samescale bar. Error bars indicate standard deviations from threeindependent measurements.

FIG. 5 is a plot showing fog harvesting performance of superhydrophobicsurface (SHS), slippery liquid-infused porous surface (SLIPS) andslippery rough surface (SRS). SLIPS has a flat surface, while SHS andSRS have the depth of 19 μm. Error bars indicate standard deviationsfrom three independent measurements.

FIGS. 6a-6d show the characterization of nanotextured micropillars. FIG.6a shows patterned nanotextured micropillars; FIG. 6b shows nanotextureson top and side walls of a micropillar; FIG. 6c is a top view of thenanotextures; FIG. 6d is a cross section of nanotextured micropillars.

FIGS. 7a-7d shows the lubrication results of a textured surface having aplurality of raised elements in the form of micropillars. FIG. 7a is across section of the lubricated micropillars. The nanotextures weresubmerged in lubricants. FIG. 7 b, c, d show ESEM image of the lubricantdistribution: spin speed 3000, 5000 and 12000 rpm. The spin time is 60seconds. Notice that at spin speeds higher than 8000 rpm, the lubricantuniformly covers the nanotextures, yielding a slippery rough surface.Depending on the viscosity of the lubricant, the spin speed and speedduration will be adjusted accordingly.

FIGS. 8a-8f show the contact angles of water droplets on Krytox 101lubricated microstructures. FIG. 8a has a Krytox 101 infusednanotextured plain surface. FIGS. 8b-f show wetting on Krytox 101lubricated micropillars at different spin speeds. 10 μL water dropletswere used in the measurements. The non-lubricated micropillar dimensionsare: w=47 μm, L=53 μm, h=19 μm.

FIG. 9 is a chart showing the retention forces of water droplets on thelubricated rough surfaces with different pillar heights. Error barsrepresent the standard deviation for three independent measurements.

FIGS. 10a-10b are charts showing the wrapping layer effect on the liquidrepellency of slippery rough surfaces FIG. 10a shows lubrication withKrytox 101 and FIG. 10b shows lubrication with mineral oil. Error barsrepresent the measurement error for a single water droplet.

FIGS. 11a-11b show contact angles for various lubricants. FIG. 1a plotscontact angle hysteresis of water droplet on various lubricants; andFIG. 11b plots experimental contact angle and the prediction of modifiedYoung's equation.

FIG. 12 is a plot showing the comparison of liquid repellencyperformances between slippery rough surfaces (in both Cassie and Wenzelstate) and superhydrophobic surfaces after the surfaces have beensubmerged into the bacterial solutions at specific period of time. Notethat the dotted line indicated that the water droplets wet and pin ontothe superhydrophobic surface.

DETAILED DESCRIPTION OF THE DISCLOSURE

The present disclosure relates to a substrate having a textured surfacethat can maintain and/or advance droplet mobility in both the Cassie andWenzel states, e.g., a slippery rough surface (SRS). Advantageously, thetextured surface includes a plurality of raised first elements and aplurality of second elements thereon and a conformal lubricant layerover the plurality of raised first elements and covering the pluralityof second elements, e.g. between and fully covering the plurality ofsecond elements. The plurality of raised first elements have an averageheight of between 0.5 μm and 500 μm, e.g., an average height of between15 μm and 100 μm. The plurality of second elements have an averageheight of between 0.01 μm and 10 μm, e.g., an average height of between0.5 μm and 5 μm. For example, the surface roughness R is between 1 and1.4 in FIG. 2 f.

The substrate can further comprise a silanized coating between theconformal lubricant layer and either the plurality of raised firstelements or the plurality of second elements or both. As used hereinsilanization means to contact the surface of the substrate with at leastone reactive silane to chemically react the surface of the substrate andthus bind the silane to the substrate surface. A silanized coatingresults from such silanization. Reactive silanes that can be used forsilanization are known in the art and include, for example,heptadecafluoro-1,1,2,2-tetrahydrodecyltrichlorosilane,trimethylchlorosilane, perfluorinated silanes, etc.

In one aspect of the present disclosure, the textured surface includes aplurality of raised elements and a conformal lubricant layer over theplurality of raised elements, wherein the conformal lubricant layer hasa uniform thickness over the plurality of raised elements, which haverandom or regular distributions. In other embodiments, the conformallubricant layer forms an energetically stable and atomically smoothlubricant layer. The plurality of raised first elements have an averageheight of between 0.5 μm and 500 μm. The height is determined from thebottom and top of a single structure.

The conformal lubricant layer can be one or more of an oleophobiclubricant, an oleophilic lubricant, a hydrophobic lubricant and/or ahydrophilic lubricant. For example, the conformal lubricant layer can betertiary perfluoroalkylamines (such as perfluorotri-npentylamine, FC-70by 3M; perfluorotri-n-butylamine FC-40, etc.), perfluoroalkylsulfidesand perfluoroalkylsulfoxides, perfluoroalkylethers, perfluorocycloethers(like FC-77) and perfluoropolyethers (such as KRYTOX family oflubricants by DuPont), perfluoroalkylphosphines,perfluoroalkylphosphineoxides and their mixtures can be used for theseapplications, as well as their mixtures with perfluorocarbons and anyand all members of the classes mentioned. The thickness of the lubricantlayer is preferably between 0.01 μm and 10 μm, which is close to theheight of the nanotextures in certain embodiments. The uniformity of thelubricant layer over the raised plurality of elements is preferably lessthan 10 μm.

The lubricant and silanization agent can be matched to a givensubstrate. For example, perfluorinated oils and perfluorinated silanescan be a combination on the substrate. Hydrophobic combination include,for example, mineral oils, hydrocarbons, and trimethylchlorosilane andhydrophilic combinations include, for example, hydroxyl PDMS andtrimethylchlorosilane.

Substrates and textured surfaces that can be used in the presentdisclosure include those of silicon, metals (e.g., copper, aluminum,steel, titanium etc. and their alloys, e.g., stainless steel, etc.),ceramics (e.g., glass), and polymers or other materials.

Advantageously, substrates having a textured surface, e.g., a slipperyrough surface, of the present disclosure can be used in a variety ofdevices. For example the substrates having a textured surface of thepresent disclosure can be used in evaporators, condensers, heatexchangers, water and oil collector devices, and drag reduction andanti-biofouling coatings.

The physical origin for the immobility of Wenzel droplets is due topinning, which results from the interaction of the liquid contact lineand micro- and nanoscopic sharp edges of the surface textures. Pinningcan be minimized by creating a molecularly smooth surface textures withround edges, but such an idealized rough surface is extremelychallenging to manufacture even with the most advanced micro ornanofabrication techniques. A recently created pitcher-plant-inspired,pinning-free surface called slippery liquid-infused porous surfaces(SLIPS) or slippery pre-suffused surfaces directly resembles anidealized smooth surface at the macroscale. SLIPS was designed to createa defect-free, ultra-smooth interface by fully infusing a texturedsurface with a liquid lubricant overcoat. The overcoat lubricant layerserves as a molecularly smooth surface that minimizes pinning of liquidcontact lines.

In contrast, the slippery rough surfaces in the present disclosure mimican idealized rough surface. Based on these surfaces, impregnated liquiddroplets can show high droplet mobility on hierarchically micro- andnano-textured surfaces in which the nanostructures alone are infusedwith lubricant (FIG. 1c ). We show that by infusing amicroscopically-thin conformal layer of lubricant on the surfacenanotextures, the sharp edges can be smoothened by the liquid lubricantand the pinning effect can be greatly reduced, leading to enhanceddroplet mobility in both Wenzel and Cassie states (FIGS. 1d, 1e ).

In practicing the present disclosure, a slippery rough surface can beprepared by texturing a surface of a substrate with a plurality ofraised first elements and a plurality of second elements thereon; andapplying a lubricant layer over the plurality of raised first elementsand fully covering the plurality of second elements. Advantageously, thelubricant can be applied to form a conformal lubricant layer over theplurality of raised first elements and preferably with a uniformthickness. Preferably the thickness of the conformal lubricant layer isbetween 0.01 μm and 10 μm. In addition, it is preferable that thethickness does not vary over the plurality of raised elements by morethan 100%.

To create a slippery rough surface with a thermodynamically stable andconformal lubricant layer, three engineering criteria should besatisfied. First, the rough surfaces should allow the lubricant tostably wet and conformally adhere to the solid textures. Second, itshould be energetically more favorable for the lubricant, rather thanforeign liquids, to wet the solid textures. Third, the lubricant andforeign liquids should be immiscible.

The first criterion can be satisfied by creating nanoscale textures onmicropillars, thus forming hierarchical structures, i.e., a plurality ofraised first elements and a plurality of second elements thereon. Inorder to describe the surface roughness (defined as the ratio of theactual to the projected surface areas) of these dual length scalestructures, we define R as the roughness resulting from the micropillarsalone, and r as the roughness resulting from nanotextures on themicropillars. The increased surface area due to roughness together withthe chemical affinity between the substrate and the lubricant (i.e., theintrinsic contact angle between the lubricant and the substrate is lessthan 90°) will enhance the wetting of lubricant.

The second criterion can be satisfied by choosing an appropriate solidand lubricant combination for an immiscible foreign fluid such that thefollowing relationships are satisfied:

r(γ_(B) cos θ_(B)−γ_(A) cos θ_(A))−γ_(AB)>0 and r(γ_(B) cos θ_(B)−γ_(A)cos θ_(A))+γ_(A)−γ_(B)>0,  (1)

where γ_(A) and γ_(B) are, respectively, the surface tensions for theforeign liquid and for the lubricant; γ_(AB) is the interfacial tensionbetween the foreign liquid and lubricant; θ_(A) and θ_(B) are theequilibrium contact angles for the foreign liquid and the lubricant on agiven flat solid surface, respectively. These relationships dictate thesolid-lubricant combinations and the required surface roughness to forman energetically stable lubricating film within the nanotextured solidthat will not be displaced by the external fluid.

As a demonstration, we chose perfluorinated silanes to functionalize thesilicon hierarchical textures and perfluorinated lubricants (i.e.,DuPont™ Krytox oils) for the lubrication. Note that perfluorinatedlubricants are known to be immiscible to both the aqueous and oilphases, and are hydrophobic in nature. The measured intrinsic contactangle, θ, of water droplets on a smooth slippery surface lubricated withperfluorinated lubricant is 121.1°±1.0°. These solid-lubricantcombinations satisfy the relationship outlined by Eq. 1 when specificcontacting fluids were used. The height of the silicon nanotextures is5.1 μm on the top of the micropillars, and 3.8 μm on the side wall. Theroughness of the nanotextures, r, was estimated to be 14.6±0.3 on theside of the micropillar and 19.3±0.4 on the top of the micropillarthrough image analysis of high resolution scanning electron micrographs.The lubricant was applied onto the solid substrate by a spin-coatingprocess, where excess lubricant was removed from the micropillarstructures at high spin speed. Due to the dominance of capillary forceper unit volume at smaller length scales, the nanotextures will helpretain the lubricant more favorably compared to the microscopicroughness. Furthermore, the strong chemical affinity of the silanecoatings to the perfluorinated lubricant together with the highroughness of the nanotextures allowed the lubricant to completely infusethe nanotextures and formed a conformal layer over the micropillarstructures (see FIGS. 2b and 2c ). The surface morphology of themicropillars was smooth with round edges as confirmed by high-resolutionelectron microscope. The non-lubricated and lubricated micropillars havesimilar surface morphology based on the cross sectional images (FIGS. 2dand 2e ) and ESEM images (FIG. 2c ).

We further quantified the surface retention behaviors of water dropletsin different wetting states on the lubricated rough surfaces. For aliquid droplet to move on a surface tilted at an angle α, the tangentialcomponent of the gravitational force, F_(gt), acting on the droplet hasto exceed the surface retention force, F. Specifically, the tangentialgravitational force and the surface retention force acting on thedroplet can be respectively expressed as,

F _(gt) =ρVg sin α and F=γD(cos θ_(R)−cos θ_(A)),  (3)

where ρ, γ, V, and D are the density, surface tension, volume, andwetting width of the liquid droplet, respectively; θ_(A) and θ_(R) arethe advancing and receding contact angles, respectively; g is theacceleration due to gravity.

To quantify the force required to initiate the droplet motion, wegradually increase the tilting angle α until the water droplet begins toslide (i.e., F_(gt)=F). We compared the retention forces of Wenzel statedroplets on the non-lubricated and lubricated surfaces. Wesystematically changed the surface roughness and measured thecorresponding F. For lubricated surfaces with h=0 (or R=1), lubricantcompletely covered the nanoscopic posts forming a flat and molecularlysmooth interface, yielding a SLIPS. Note that F for a Cassie droplet isdefined as the retention force of a Cassie droplet on non-lubricatedmicropillars (w=L=50 μm, h=20 μm).

The measured F increases linearly with surface roughness R (FIG. 2f ) onlubricated surfaces. This indicates that the retention force for adroplet in the Wenzel state on lubricated surfaces is linearlyproportional to the liquid-lubricant contact area (or F∝R).Interestingly, the retention force of Wenzel droplets on the lubricatedsurface could be smaller than that of the Cassie droplet on anon-lubricated surface with the same solid fraction (FIG. 2f ). This isbecause the retention force of a Cassie state droplet primarily resultsfrom pinning of the liquid contact line at the sharp edges of the solidtextures. With the smoothened edges on a lubricated rough surface, thepinning is greatly minimized and thereby leads to significantly reducedsurface retention force of liquid droplets regardless of their wettingstates.

To further generalize our results, we examined the droplet mobility of abroad range of aqueous and organic liquids with surface tensions rangingfrom ˜72.4 mN/m to ˜19.9 mN/m on the lubricated rough surfaces (FIGS.4a-4e ). Results show that Wenzel droplet mobility on the slippery roughsurfaces is maintained even for liquids with low contact angles. Forexample, hexadecane drops (γ=27.4 mN/m, θ=84.4°) are highly slippery onthe lubricated rough surface (FIGS. 4a and 4b ), but are strongly pinnedon the silanized non-lubricated micropillars (FIGS. 4c and 4d ). Whilelower surface tension liquids (i.e., heptane) exhibit higher retentionforces than higher surface tension fluids (i.e., water), these liquidsstill maintain high drop mobility on the lubricated rough surfaces. Tocompare the relative magnitude of the retention force on lubricated andnon-lubricated substrates, we define F* as the retention force of theWenzel state droplet on lubricated micropillars normalized by that onnon-lubricated ones with the same surface roughness. F* ranges from ˜10%for high surface tension (72.4 mN/m) fluids to ˜36% for low surfacetension fluids (19.9 mN/m). In other words, the measured retention forcevalues of Wenzel drops on these lubricated surfaces are significantlylower than those on non-lubricated surfaces (FIG. 4e ). This isattributed to the reduction of pinning through smoothening ofmicro/nanoscopic edges by the lubricant. These results demonstrate thatlubricated rough surfaces can substantially reduce retention force andthus enhance drop mobility of Wenzel drops with various surfacetensions.

Our experimental results demonstrate that lubricated rough surfaces arecapable of maintaining droplet mobility regardless of wetting state. Itis important to note that Cassie-to-Wenzel transition can be easilyinduced on any textured surfaces, e.g., by high pressure, hightemperature, low surface tension, surface contamination, for example.Such a transition will eventually render the liquids immobile onnon-lubricated rough surfaces. While tremendous efforts have beeninvested in preventing or delaying the transition to the Wenzel state,our results show that one can circumvent this challenging issuealtogether by simply coating a conformal layer of liquid lubricants onrough solid textures; doing so allows liquid droplets to maintain theirmobility in both Cassie and Wenzel states. Thus, the slippery roughsurfaces of the present disclosure can effectively circumvent theWenzel-to-Cassie transition challenge, creating a simpler method ofmaintaining drop mobility.

The ability to repel liquids regardless of how they wet the roughsurface has important technological implications for many industrialprocesses from condensation heat transfer to water harvesting to theprevention of icing and frosting. In certain applications, a slipperyrough surface would be highly desirable due to its high surface area andslippery interface. To illustrate embodiments of the present disclosure,we have demonstrated application examples in fog harvesting andcondensation using the slippery rough surfaces, and have shown thatthese surfaces outperform the state-of-the-art superhydrophobic surfaces(SHS) and SLIPS.

In the first application example, we experimentally studied the fogharvesting rate on SHS (i.e., in the form of silanized hierarchicalmicrochannels), SLIPS (i.e., lubricant infused nanotextures), and theslippery rough surfaces introduced in this effort (i.e., in the form ofconformally lubricated microchannels) (FIG. 5). The surface structureswere designed in the form of microchannels to enhance the effect ofcapillary wetting. The channel and pillar widths for microchannels wereboth 50 μm, with a depth ranging from 20 to 50 μm. In this experiment,hydroxy polydimethylsiloxane (PDMS) was used as the lubricant due to itsrelatively hydrophilic nature for enhanced capillary wetting. Theslippery rough surface (of depth ˜20 μm) exhibited a fog harvesting rateof 376.0 mg/(hr·cm²) (mg—milligram, hr—hour, cm—centimeter), which is22.2% faster than SLIPS and 136.8% faster than SHS (FIG. 5). Owing tothe higher surface area relative to SLIPS, the slippery rough surfaceexhibited enhanced drop nucleation and coalescence, resulting in fasterdroplet removal. On SHS, microscopic liquid droplets were pinned ontothe surface structures due to large Laplace pressure of the smalldroplets. As a result, SHS displayed a much smaller droplet removal ratecompared to that of slippery rough surfaces. By increasing the depth ofthe microchannel from 20 μm to 50 μm, the fog harvesting rate onslippery rough surfaces increased by 11.1% (FIG. 5). This indicates thatfog harvesting performance can be further optimized by engineering thedimensions of surface structures.

In another set of application-oriented tests, we studied phase-changeprocesses such as dropwise condensation on the slippery rough surfacesusing ESEM. The samples were maintained at −5° C. under a water vaporpressure of 3.8 torr (the associated saturation temperature is −2.5° C.)to facilitate the condensation process. While slippery rough surfaceshave smaller surface areas compared to SHS, the drop mobility is higherdue to the lubricated surface boundary. As a result, the slippery roughsurfaces remove the condensates faster and further expose water-freeareas for the next condensation cycle. Compared to SLIPS, slippery roughsurfaces have larger surface areas, which greatly enhance the dropletnucleation and removal rates. These microscopic observations furthervalidate and support the superior fog harvesting ability of slipperyrough surfaces at the macroscale. These results indicate that slipperyrough surfaces outperform state-of-the-art liquid repellent surfaces forfog harvesting and dropwise condensation functions owing to their highsurface area and slippery interface.

In yet another set of application-oriented tests, we studied the oiladsorption ability of the slippery rough surface (in the form oflubricated aluminum meshes). Unlike conventional design of oil-waterseparating membranes, our mesh has the ability to repel almost allliquids, which overcomes the fouling problem of conventional oiladsorbents. To demonstrate the oil absorbing ability of the slipperyrough surfaces, a lubricated mesh was put into an oil-water solution,which has already been separated into two distinct layers. We first dyedthe mineral oil (Sigma Aldrich) to enhance visibility and mixed it withwater. To separate mineral oil with water, we put the lubricated meshscreen into the mixture for a period of time. The mineral oil wasabsorbed on the mesh screen due to the superoleophilic nature of thelubricated mesh. Then we quickly take off the mesh screen from themixture. The absorbed oil dripped off from the mesh completely due tothe presence of the slippery interface, demonstrating to itsanti-fouling property. Therefore, the lubricated mesh can be recycledwithout or with minimal cleaning requirement. Additionally, the mesh cancollect oil in oil-water emulsion without any fouling.

In contrast to the well-established physical concept that a droplet inthe Cassie state is mobile and a droplet in the Wenzel state is sticky,our study shows the conceptually different perspective that both Cassieand Wenzel droplets can be mobile. Not only is the identification of theslippery Wenzel state of fundamental importance, these new findings canbe used to design a new type of liquid repellent strategy for manyindustrial applications where enhancing droplet mobility and removal isimportant. While our work used silicon as an example, the designprinciple can be easily extended to other material systems such asmetals, glasses, ceramics, and plastics owing to the diverse fabricationtechnologies available to create hierarchical surface architectures.Moreover, one can engineer the composition of the coatings (e.g.,viscosity or phase change temperatures of lubricants) for their uses indifferent environmental conditions, such as extreme temperature orhumidity. The longevity of the lubricated rough surfaces can beengineered by choosing lubricants with low evaporation rate, lowmiscibility, and reduced wrapping of the lubricant around the contactingfluid. When necessary, the longevity of the lubricants could be furtherenhanced by infusing these lubricants into polymeric coatings asreservoirs. Since our slippery rough surfaces combine the uniqueadvantages of superhydrophobic surfaces (i.e., high surface area) andSLIPS (i.e., slippery interface) and can repel liquids in any wettingstate, these surfaces will find important industrial applicationsrelated to liquid harvesting, liquid absorption/separation, and phasechange applications. For example, the slippery rough surfaces couldfurther enhance condensation heat transfer as compared tosuperhydrophobic surfaces, even in relatively high temperatureenvironments such as those that exist in heat exchangers or organicRankine cycles. In icing condition, the lubricated rough surfaces couldreadily shed off liquid condensates in the Wenzel state to delay frostand ice formation. These lubricated rough surfaces could provide waterharvesting in high humidity conditions faster than the state-of-the artliquid-repellent surfaces. Many of these water condensates havetraditionally pinned to the surface texture—a result of irreversibletransition from the Cassie state to the “sticky” Wenzel state. Inaddition, the lubricated rough surfaces can also serve as drag reductionand anti-biofouling coatings. The ability to repel fluids in any wettingstate may open up new opportunities for scientific studies andengineering applications related to adhesion, nucleation, transportphenomena, and beyond.

Examples

The following examples are intended to further illustrate certainpreferred embodiments of the invention and are not limiting in nature.Those skilled in the art will recognize, or be able to ascertain, usingno more than routine experimentation, numerous equivalents to thespecific substances and procedures described herein.

When a liquid droplet rests on top of a roughened surface and thedroplet has not impregnated the surface textures but rather gas fillsthe textures, the droplet is in the Cassie state. Our substrates arehierarchically structured such that lubricant fills the nanostructures,while gas fills the microstructures, thus creating a conformal lubricantlayer on the microstructures. We consider a liquid droplet that does notimpregnate the microtextures to be in the Cassie state. We havedemonstrated that our slippery rough surfaces still maintain highdroplet mobility in the Cassie state on these slippery rough surfaces.

Fabrication and Characterization of Nanotextured Micropillars.

Square-shaped silicon micropillars were fabricated using standardphotolithography and deep reactive-ion etching (DRIE) on a 4 inch <100>p-type silicon wafer with a thickness of 400 μm. Then the photoresist onthe top surfaces and polymer on the side walls of micropillars wereremoved by oxygen plasma. A wet etching method was used to createnanotextures on the surfaces of square micropillars. The microstructuredsilicon wafer obtained from the previous step was cleaned in Piranhasolution to remove the organics and then in the 5% hydrofluoric acid(HF) solution for 20 seconds to remove the oxide layer. Subsequently,the wafer was immediately immersed into a solution of 4.8 M HF and 0.01M silver nitride (AgNO₃) for 1 min to deposit catalysts. The Ag⁺ wasreduced to Ag nanoparticles, which could be deposited on the top, bottomand side walls of the microstructured silicon surfaces. These Agnanoparticles acted as catalysts to enhance local etching speed duringthe etching process. The microstructured wafer with the catalyst was putin the etching solution containing 4.8 M HF and 0.3 M hydrogen peroxide(H₂O₂) for 6 to 7 min. After the catalyst deposition and etching step,the wafer was placed into the dilute nitric acid solution to dissolvethe silver dendrites. In the end, the wafer was washed with DI water anddried with nitrogen gas. Patterned nanotextured micropillars wereobtained on the silicon wafer (FIGS. 6a, b and c ). The height of thenanotextures is 5.1 μm on the top of the micropillars and 3.8 μm on theside wall, respectively (FIG. 6d ). The roughness of the nanotextureswas estimated to be 14.6±0.3 on the side of the micropillar and 19.3±0.4on the top of the micropillar through image analysis of high resolutionscanning electron micrographs. Image analyses were conducted usingMATLAB. The greyscale image (i.e., an image with pixel intensitiesranging over a spectrum from 0 to 1, where 0 is black and 1 is white)shown in FIG. 10c was converted to a binary image (i.e., where pixelintensities are either 0 or 1) based on a set intensity threshold. Toensure that we chose an intensity threshold such that nanotexture topswere captured as white area and the rest of the image was captured asblack area, we calculated the roughness at 40 different threshold valuesfrom 0 to 1. A plateau in the roughness versus threshold value occurredapproximately between a threshold of 0.2 and 0.4, so the average ofroughness values between these points was used as the roughness. Toensure that 40 threshold points yielded an appropriate resolution, thisaverage roughness was calculated for varying resolutions untilconvergence was apparent, and a resolution of 40 points proved to besufficient.

Fabrication of Nanotextured Aluminum Mesh

Nano-textured aluminum meshes were fabricated by two-step etchingprocesses. The aluminum mesh was washed by diluted hydrochloric acid for10 min to remove the oxidized layer on the surface. Then steam was usedto oxidize the mesh for 1 hour in atmospheric pressure (101 kPa) to formboehmite nanotextures. The mesh wire is uniformly etched withnanotextures, which is helpful to enhance the hydrophobicity and thelubricant retention on the surface. The diameter of the mesh wire variesfrom 53 μm to 400 μm. The nano boehmite structure on the wire has adepth of tens of nano meters.

Silanization and Lubrication.

The nanotextured silicon microstructures/aluminum mesh were silanizedusing either heptadecafluoro-1,1,2,2-tetrahydrodecyltrichlorosilane(Gelest Inc.) or trimethylchlorosilane (Sigma-Aldrich). These silaneswere deposited onto the silicon surfaces in a vacuum chamber for 4hours, and were deposited onto aluminum mesh in ethanol solution for 20hours, or less time with higher temperature Afterwards, lubricant suchas Krytox 101 (DuPont, viscosity of 17.4 cSt at 20° C.) was coated onthe silanized nanotextured micropillars using a spin coater. Thelubricant thickness was controlled by the spin speed of the spin coater.Higher spin speed can remove more lubricants and yield a lubricant layerthat is more conformal to the micropillars. The cross sections ofmicropillars were visualized by a goniometer. Increased spin speed helpsto remove the lubricants between two micropillars as shown in the ESEMimages of FIG. 7 a.

Experimental Verification of Stable Lubricated Film Formation

We conducted further analysis to show that conformal lubricant coatingcan be achieved on the microstructures for all solid-lubricantcombinations against various contacting fluids investigated in thiswork. In order to form a thermodynamically stable lubricant layer withinthe nanotextures, the solid-lubricant combination should satisfy thefollowing relationships^(3,24):

ΔE ₁ =r(γ_(B) cos θ_(B)−γ_(A) cos θ_(A))−γ_(AB)>0  (Eq. S1)

ΔE ₂ =r(γ_(B) cos θ_(B)−γ_(A) cos θ_(A))+γ_(A)−γ_(B)>0  (Eq. S2)

where r is the roughness of the nanotextures; γ_(A) and γ_(B) are,respectively, the surface tensions for the foreign liquid (Liquid A) andfor the lubricant (Liquid B); γ_(AB) is the interfacial tension betweenthe foreign liquid and lubricant; θ_(A) and θ_(B) are, respectively, theequilibrium contact angles for the foreign liquid and the lubricant on aflat solid surface. These relationships dictate the solid lubricantcombinations that form an energetically stable lubricating film withinthe textured solid without being displaced by an external fluid. Ourexperimental measurements (Table 1) confirmed that thesolid/lubricant/foreign liquid combinations used in our experimentsfulfilled the requirements outlined by Eqs. S1 and S2 (i.e., ΔE₁>0 andΔE₂>0).

TABLE 1 Theoretical and experimental verifications for the formation ofthe stable conformally lubricated microstructures. Stable? Solid LiquidA Liquid B r γ_(A) γ_(B) γ_(AB) θ_(A) θ_(B) ΔE₁ ΔE₂ Theory Exp.Silanized Water Krytox 101 14.6 72.4 17.0 56.4 121.3 42.3 675.7 787.5 YY silicon-1 Silanized Glycerol Krytox 101 14.6 60.1 17.0 40.5 122.6 42.3615.6 699.2 Y Y silicon-1 Silanized Ethylene glycol Krytox 101 14.6 48.217.0 28.1 112.4 42.3 423.5 482.8 Y Y silicon-1 Silanized HexadecaneKrytox 101 14.6 27.3 17.0 8.7 84.9 42.3 139.0 158.1 Y Y silicon-1Silanized Undecane Krytox 101 14.6 24.6 17.0 6.7 76.3 42.3 91.6 105.9 YY silicon-1 Silanized Ethanol Krytox 101 14.6 21.1 17.0 23.5 76.4 42.387.4 115.0 Y Y silicon-1 Silanized Hydrid PDMS Krytox 101 14.6 20.2 17.05.6 66.1 42.3 58.5 67.2 Y Y silicon-1 Silanized Heptane Krytox 101 14.619.9 17.0 2.7 62.8 42.3 48.0 53.6 Y Y silicon-1 Silanized Water Mineraloil 14.6 72.4 28.6 50.1 90.5 32.4 311.1 405.0 Y Y silicon-2 SilanizedWater Hydroxy PDMS 14.6 72.4 21.1 7.0 90.5 13.1 301.8 360.0 Y Ysilicon-2 Note: “Silanized silicon-1” refers to nanotexturedmicrostructures were silanized by theheptadecafluoro-1,1,2,2-tetrahydrodecyltrichlorosilane and “Silanizedsilicon-2” refers to those silanized by trimethylchlorosilane. “Y”indicates that Liquid B can form stable conformally lubricatedmicrostructures. γ_(A) and γ_(B) represent the surface tensions ofLiquid A and Liquid B, respectively (Table 2). γ_(AB) represents theinterfacial tension between Liquid A and Liquid B (Table S3). θ_(A) andθ_(B) are the static contact angles on silanized flat silicon substrate(Table 4).

TABLE 2 Measured Surface Tension for Various Polar and Non-PolarLiquids. Surface tension Number of Liquids (mN/m) measurements Water72.4 ± 0.2 5 Glycerol 60.1 ± 0.5 5 Ethylene glycol 48.2 ± 0.3 5Hexadecane 27.3 ± 0.2 5 Undecane 24.6 ± 0.3 5 Ethanol 21.1 ± 0.3 5Hydrid PDMS 20.2 ± 0.3 5 Heptane 19.9 ± 0.4 5 Krytox 101 17.0 ± 0.2 5Mineral oil 28.6 ± 0.2 5 Hydroxy PDMS 21.1 ± 0.3 5

TABLE 3 Measured Interfacial Tension between Two Immiscible Liquids.Interfacial tension Number of Liquid/Liquid (mN/m) measurementsWater/Krytox 101 56.4 ± 1.0  5 Glycerol/Krytox 101 40.5 ± 0.4  5Ethylene glycol/Krytox 101 28.1 ± 0.2  5 Hexadecane/Krytox 101 8.7 ± 0.25 Undecane/Krytox 101 6.7 ± 0.1 5 Ethanol/Krytox 101 23.5 ± 0.6  5Hydrid PDMS/Krytox 101 5.6 ± 0.2 5 Heptane/Krytox 101 2.7 ± 0.1 5Mineral oil/Water 50.1 ± 0.5  5 Hydroxy PDMS/Water 7.0 ± 0.3 5

TABLE 4 Measured Static Contact Angles of Various Liquids on SilanizedFlat Silicon. Contact angle Number of Solids Liquids (degrees)measurements Silanized flat silicon-1 Water 121.3 ± 0.9  5 Silanizedflat silicon-1 Glycerol 122.6 ± 0.4  5 Silanized flat silicon-1 Ethyleneglycol 112.4 ± 0.6  5 Silanized flat silicon-1 Hexadecane 84.9 ± 0.4 5Silanized flat silicon-1 Undecane 76.3 ± 0.5 5 Silanized flat silicon-1Ethanol 76.4 ± 0.7 5 Silanized flat silicon-1 Hydrid PDMS 66.1 ± 0.6 5Silanized flat silicon-1 Heptane 62.8 ± 0.3 5 Silanized flat silicon-1Krytox 101 42.3 ± 0.5 5 Silanized flat silicon-2 Water 90.5 ± 1.2 5Silanized flat silicon-2 Mineral oil 32.4 ± 1.1 5 Silanized flatsilicon-2 Hydroxy PDMS 13.1 ± 0.4 5

Choice of Lubricants and Silanes

In addition to the use of perfluorinated oils and fluorinated silanes,one can tune the surface hydrophobicity of the slippery rough surfacesbased on a broad range of hydrophobic and hydrophilic lubricants as longas both the Eq. S1 and S2 are satisfied. In choosing differentlubricants, the silanes coating would need to be adjusted accordingly.As a demonstration, we have shown that trimethylchlorosilane can be usedfor various hydrophilic and hydrophobic lubricants ranging from hydroxylpolydimethylsiloxane, silicone oils, hydrocarbons (e.g., hexadecane),mineral oils, hydride polydimethylsiloxane, and perfluorinated oils.These silane and lubricants combinations can be used to repel water. Forexample, FIG. 11 shows the contact angle for various lubricant/silanecoatings on a surface that does not have a dual length scalehierarchical roughness to illustrate the various combinations.

Environmental Scanning Electron Microscope (ESEM).

After the lubrication process, the nanotextures were fully submergedunder the lubricant layer. The lubricated micropillars were visualizedby an ESEM to capture the distribution of oil lubricants on an angledstage (40°˜60°). The applied voltage was 20 kV and current was 2.1 nAfor the operation of ESEM. To minimize the evaporation of oillubricants, the temperature was reduced to −5° C. before the low vacuumwas applied. The pressure was set at 3.8 torr, which is much higher thanthe saturation pressure of Krytox 101 at −5° C. From the ESEM images(FIG. 7b, c and d ), it is evident that at a spin speed of 3000 rpm, thelubricated bottom surface is exposed but the bottom corners are thicklycovered by lubricant owing to the capillary force. However, at a spinspeed of 12000 rpm, the lubricants were only retained within thenanotextures, and were completely removed from the space betweenmicropillars. The lubricated surfaces (FIG. 7d ) therefore showed asurface morphology similar to that of non-lubricated micropillars. Thewhole surface shows patterned micropillars with a conformal lubricantlayer.

In this experiment, the surface roughness was calculated based on w, L,and h (See definitions in the main text). Since the lubricant coveredthe bottom corners of the micropillars, the lubricated micropillars donot have a well-defined geometry (FIG. 7b ). We measured h from the topof the lubricated micropillar to the bottom of the lubricated surfaces.When the spin speed is 12000 rpm (FIG. 7d ), the calculated roughnessclosely resembles the actual roughness as verified by thehigh-resolution electron micrographs.

Contact Angle and Sliding Angle on Lubricated Microstructures.

The sliding angle was measured by an automated goniometer (ramé-hart) atroom temperature (21-24° C.) with ˜20% relative humidity. The system wascalibrated each time before the measurements were conducted. The imageof the droplet was captured through a camera equipped with the opticalsystem and the drop imaging software measured the contact angle, contactangle hysteresis, and the sliding angle.

In an effort to measure the contact angle under known and repeatableconditions, a lubrication protocol was established. As part of theprotocol, we coated oil lubricant onto the nanotextured micropillars(w=47 μm, L=53 μm, h=19 μm) at a spin speed of 12000 rpm. The lubricantwas trapped in the nanotextures, creating a surface with lubricatedmicropillars (FIG. 7d ). The contact angle was measured on the liquidinfused nanotextures (FIG. 8a ) and lubricated rough surfaces withdifferent lubricant thicknesses (FIGS. 8b-f ).

During the measurement, the stage was tilted automatically at the speedof 1 degree/second and the drop image was captured every second. Thesliding angle can be obtained by analyzing those images. When thecontact line starts to move, the associated tilted angle is taken as thesliding angle. The accuracy of the measurement is ±0.5°. The measuredsliding angles were used to estimate the droplet retention forces on thelubricated rough surfaces with different pillar heights (FIG. 9).

Fabrication of Nanotextured Microgrooves

Microgrooves on aluminum surface were fabricated using a standardmicromachining. The groove size and space between grooves are ˜200 μm.The aluminum residues and other surface contaminations (e.g., oils)generated from the machining were removed by ultrasonic cleaning inacetone for 15 min. An acid wash process was used to remove an oxidizedaluminum layer on the surface, which may inhibit the growth of boehmitenanotexture. The microgrooved aluminum was washed in dilutedhydrochloric acid (1 wt. %) for 10 min, and then cleaned by DI water. Awater steam etching was used to create boehmite nanotextures on thesurfaces of grooves. The microgrooved aluminum cylinder was put in awater steam environment at 100 C.° with a pressure of 105 kPa for 20min. The nanotextured microgrooves were created on aluminum cylinder.

Silanization and Lubrication

Oxygen plasma was conducted before silanization. The nanotexturedmicrogrooved aluminum cylinder was cleaned and surface activated in anoxygen plasma cleaner (Harrick) for 15 min. The nanotextured aluminummicrostructures were silanized using1H,1H,2H,2H-perfluorodecyltriethoxysilane (Sigma-Aldrich). The silanemolecules were deposited onto aluminum in ethanol solution at 80 C.° for4 hours. Afterwards, lubricant such as Krytox 101 (DuPont, viscosity of17.4 cSt at 20° C.) was coated on the silanized nanotexturedmicrogrooves by spray coating, and excess lubricant between the grooveswas removed by a nitrogen gun.

Fog Harvesting, Dropwise Condensation

The slippery rough surfaces have a wide range of applications, such aswater harvesting, dropwise condensation, advanced heat exchange, andrefrigeration. Three surfaces, including SHS (i.e., silanizedhierarchical microchannels), SLIPS (i.e., lubricant infusednanotextures) and slippery rough surfaces (i.e., microchannels withconformal lubrication) were used to compare their performance in theapplications of fog harvesting and dropwise condensation. The micro/nanohierarchical microchannels were fabricated using aforementioned DRIE andwet etching methods.

A conventional ultrasonic humidifier (Crane EE-5301) was used to producecool mist. The lubricated rough substrates were placed vertically,facing the mist. The distance between the outlet of the humidifier andthe vertical substrate was ˜15 cm. The dripping water was collected by aclean beaker. The weight of the beaker before and after collection wasmeasured as M_(b) and M_(a), respectively. The weight of the lubricatedsample before and after collection was measured as M_(sb) and M_(sa),respectively. The total mass of harvested fog in a given interval oftime was M_(f)=(M_(sa)+M_(a))−(M_(sb)+M_(b)). These measurementsaccounted for the residual water on the lubricated substrate and excludethe lubricant that was carried away by the collected water droplets.

The dropwise condensation experiment was performed on a peltier coolingstage inside an ESEM. The slippery rough surfaces were functionalized bytrimethylchlorosilane silane and lubricated by hydroxy PDMS (SigmaAldrich, viscosity 25 cSt). The lubricant thickness was controlled bythe speed of a spin coater. We used a speed of 12000 rpm as it allowedfor conformal lubrication. The chamber pressure, temperature, andhumidity in the ESEM were set to 3.8 Torr, −5° C. and 85%, respectively.The tilted angle of the sample was 50°. To minimize the evaporation oflubricant, we decreased the chamber temperature to 0° C. before weloaded the sample.

Longevity and Robustness of the Slippery Rough Surfaces

The longevity of the lubricated rough surfaces is highly reliant onthree factors, including: I) the miscibility of lubricant and thecontacting fluid, II) the evaporation rate of the lubricant, as well asIII) the wrapping of the lubricant around the contacting fluid. In orderto enhance longevity for a given application, the lubricant should bechosen for its low miscibility, low evaporation rate and reducedwrapping around the contacting fluid. There are many commerciallubricants with negligible solubility with water. For instance, thesolubilities of water in perfluorinated oils, mineral oils, and liquidpolydimethylsiloxane are 1.76 mol/m³, 2.14 mol/m³ and 36 mol/m³,respectively³⁶. In the following discussion we will focus on thelongevity characterizations of water-immiscible lubricants infused intothe slippery rough surfaces.

Evaporation of Lubricants

We studied the evaporation rates of the lubricants infused into theslippery rough surfaces using a high resolution analytical balance(Mettler Toledo XP504 DeltaRange, resolution=0.1 mg). A previous studyon SLIPS has shown that the lifetime of the lubricant variessignificantly with its viscosity and chemical composition. Based on thisstudy, we have evaluated a number of different lubricants for thelongevity tests. The lubricants under investigations includeperfluorinated oils (e.g., Krytox 101 and Krytox103, DuPont) and mineraloil. Different Krytox oils have different viscosities, ranging fromKrytox 100 to 107 with increasing viscosity and boiling point. We haveconducted experiments to monitor the evaporation of the lubricants onthe lubricated rough surfaces under static, ambient conditions. Wedefine the relative mass of lubricant, M*, as the residual lubricantweight in the textures at an instant in time M(t) normalized by theoriginal lubricant weight M₀, i.e., M*(t)=M(t)/M₀, where t is time.Consistent with the earlier study, we found that the relative mass ofKrytox 101 reduced by about 35% over the course of 14 days, while thatof Krytox 103 or mineral oil only reduced by about 5-10% during the sameperiod of testing. These results support that choice of lubricantproperties influence lubricant longevity.

To further study the effect of lubricant evaporation on the liquidrepellency of the lubricated rough surfaces, we continued to study thedrop mobility on the Krytox 101, Krytox 103, and mineral oil lubricatedrough surfaces. Consistent with our lubricant evaporation data, therough surfaces lubricated with Krytox 101 showed noticeable degradationof liquid repellency over the course of 14-days as exhibited by thesignificant increase in the sliding angle (i.e., an increase of 9degrees). In comparison, both of the rough surfaces lubricated by Krytox103 and mineral oil showed consistent liquid-repellency performancewithin our 14-day experimental time frame (i.e., an increase of <3degrees). Our experimental data further supported that the longevity ofslippery rough surfaces can be engineered by selecting appropriatelubricants for specific applications.

Wrapping Layer: Lubricants Spreading onto Contacting Fluid

A third factor impacting the longevity of the slippery rough surfaces isthe lubricant wrapping layer around the contacting fluid droplet. Whenconsidering lubricant-droplet interactions, it is important to determinewhether the lubricant forms a wrapping layer around the droplet. Suchinformation is important because the formation of a wrapping layerimplies the loss of lubricant volume as the droplet slides off of thelubricated surface. This lubricant loss leads to an undesirable decreasein the liquid repellency of the surface. To determine whether a wrappinglayer forms, we assume that the surface energy of thesubstrate-lubricant-droplet system is minimized. Consider a system wherea liquid droplet sits on a lubricant-infused surface. We assume that thedroplet and the lubricant are immiscible and that the droplet does notdisplace the lubricant. Let the surface energy associated with thedroplet with no wrapping layer be E₁. The energy state is thereforegiven by:

E ₁=γ_(l) ₁ _(v) A ₁+γ_(l) ₁ _(l) ₂ A ₂  (Eq. S3)

where γ_(l) ₁ _(v) is the surface tension of the contacting fluiddroplet in vapor and γ_(l) ₁ _(l) ₂ is the interfacial tension betweenthe contacting fluid droplet and lubricant. A₁ is the area of thedroplet-vapor interface and A₂ is the area of the droplet-lubricantinterface. Now we consider a similar case where the droplet has a fullor partial lubricant wrapping layer surrounding the droplets. Assumingthat the wrapping layer is thin such that the area A₁ of the droplet isapproximately constant, the energy state of this droplet is:

E ₂=γ_(l) ₁ _(v)(1−β)A ₁+γ_(l) ₂ _(v) βA ₁+γ_(l) ₁ _(l) ₂ (βA ₁ +A₂)  (Eq. S4)

where β is the fraction of A₁ coated with a lubricant wrapping layer andγ_(l) ₂ _(v) is the surface tension of the lubricant in vapor. In orderto prevent a wrapping layer, the former system must be energeticallymore favorable than the latter. Specifically, the criterion for thenon-existence of a full wrapping layer is:

E ₁ <E ₂

γ_(l) ₂ _(v)−γ_(l) ₂ _(v)−γ_(l) ₁ _(l) ₂ <0  (Eq. S5)

TABLE S5 In our experiments, we consider the vapor phase to be air.Droplet Surface Lubricant Lubricant/Droplet Tension Surface TensionInterfacial Tension Wrapping Lubricant Droplet (mN/m) (mN/m) (mN/m) Eq.S3 Layer? K101 Water 72.4 ± 0.1 17.0 ± 0.3 55.3 ± 0.5   0.1 ± 0.9 < 0Yes/No K103 Water 72.4 ± 0.1 17.8 ± 0.3 56.3 ± 0.5 −1.7 ± 0.9 < 0 NoMineral Oil Water 72.4 ± 0.1 28.6 ± 0.3 50.1 ± 0.5 −6.3 ± 0.9 < 0 No

Based on Eq. S5, we predicted the possible formation of full wrappinglayers of various lubricants around water (the contacting fluid). Wemeasured the surface tension of water and the lubricants, as well as thelubricant-water interfacial tensions in order to obtain the predictions.It is predicted that Krytox 101 may form a wrapping layer around a waterdroplet whereas Krytox 103 and mineral oil should not (Table S5).

Based on the predictions, we conducted multiple sliding dropletexperiments to evaluate the wrapping layer effect on the longevity ofthe slippery rough surfaces. In line with the prediction, dropping waterdroplets continuously on the rough surfaces lubricated with Krytox 101degrades the surface over time as indicated by the increasing slidingangle (FIG. 10a ); the rough surfaces lubricated with mineral oil didnot degrade over time (FIG. 10b ). When necessary, the longevity of thelubricants can be further enhanced by infusing these lubricants intopolymeric coatings serving as reservoirs.

Anti-Biofouling Properties of Slippery Rough Surfaces

Anti-biofouling surfaces are of interest in various fields from medicineto seafaring ship design. In medicine, anti-fouling surfaces wouldprolong the lifetime of medical devices such as catheters and reduce thespread of disease via surface contamination. In naval applications, suchsurfaces would prevent barnacle buildup on ships and thus reduce dragand wasted energy. While conventional superhydrophobic surfaces cansuccessfully prevent bio-fouling for short periods of time (i.e., a fewhours), organisms such as bacteria can still adhere to the solid surfaceeventually eliminating its anti-fouling capabilities. Other methods foranti-fouling coatings are to incorporate chemicals such as copper and/orco-biocides to prevent fouling. These options are less than ideal,however, as they either contribute to the rise of “super-bugs” or maypose environmental hazards.

Slippery rough surfaces address anti-fouling through a differentmechanism a mechanism similar to that of slippery liquid-infused poroussurfaces (SLIPS). The conformal liquid layer inhibits bio-foulingbecause there is no solid surface onto which organisms (such asbacteria) can attach. If they do settle onto the lubricant layer of theSRS, they can be easily removed via shear force as the lubricant layeris mobile.

To assess the anti-biofouling properties of SRS and compare theiranti-fouling performance to conventional surfaces, we immersed thefollowing surfaces in static (i.e., non-flowing) media containing thesame starting concentration of Escherichia coli: porouspolytetrafluoroethylene (PTFE) membrane with 200 μm pore sizes, the samePTFE membrane material infused with Krytox 101 (or SLIPS), asuperhydrophobic surface on which a water droplet would be in the Cassiestate, and a SRS with the same geometry as the SHS surface and on whicha water droplet would be in the Cassie state, and a SRS surface in whicha water droplet would be in the Wenzel state. We measured the slidingangle of a 100 μL droplet on each at different instants in time, andalso checked the absorbance of the bacteria medium to 600 nm wavelengthlight as a means of quantifying the bacteria density. Superhydrophobicsurfaces on which a water droplet would be in the Wenzel state wereexcluded from this experiment as the sliding angle of a droplet on thissurface is very high before even being exposed to the bacteria medium.Moreover, we took samples of the media and dyed the bacteria every 24hours to determine if the bacteria were thriving (and thus able toadhere to the surfaces).

Our results show that the liquid repellency of the PTFE membrane breaksdown after only 3 hours, and SHS shows signs of contamination after 3hours. After 24 hours of incubation, the liquid repellency of SHS iscompletely damaged. In contrast, SRS shows persistent anti-biofoulingperformance even after >70 hours immersion inside the bacteria media.The biofilm that is formed onto the surface can be removed spontaneouslyby the motion of a water droplet tilted at <20° with respect to ahorizontal surface, indicating very low adhesion of the biofilm with thesurface.

Drag Reduction on Slippery Rough Surfaces

Slippery rough surface can reduce friction and save energy for marineships. We design the slippery rough surface in a way such that air canbe trapped within the lubricated micropillars to maintain water flow inthe Cassie state. In this particular example, we designed the slipperyrough surfaces with square micro pillars (width=15 μm, height=50 μm,pitch size=40 μm), which were covered with water-immiscible liquidlubricants.

In order to demonstrate the feasibility of slippery rough surfaces toreduce drag, we have measured the slip lengths of the surface by arheometer using the published protocols. See C.-H. Choi and C.-J. Kim,“Large Slip of Aqueous Liquid Flow over a NanoengineeredSuperhydrophobic Surface,” Phys. Rev. Lett., vol. 96, no. 6, p. 066001,February 2006. Slip length is a measure of drag reduction capability ofthe surface to a specific test liquid and is independent of dimensionsof the flow field. In particular, the slip length of a fluid across asurface can be estimated from the torque measurement by a rheometer. Thetorque, M, is related to the slip length, b, by the following equationderived from the Navier-Stoke equation using Navier's assumption thatslip velocity is proportional to the shear rate at the wall,

$M = {\frac{2\; \pi \; \mu \; \Omega \; R^{3}}{3\; \theta_{0}}\left( {1 - \frac{3b}{2R\; \theta_{0}} + \frac{3b^{2}}{R^{2}\theta_{0}^{2}} - {\frac{3b^{3}}{R^{3}\theta_{0}^{3}}{\ln \left( \frac{{R\; \theta_{0}} + b}{b} \right)}}} \right)}$

where μ is fluid viscosity, R is the cone radius, Ω is the angularvelocity of the cone, and θ₀ is the cone angle.

To measure the torque M, a commercial rheometer (DHR-2, TA Instruments)was used which has a stainless steel cone with 40 mm diameter and 1°cone angle. The torque was measured under a constant shear rate 100 s⁻¹.The test fluid is water.

The liquids viscosity μ in (eq.1) were measured through controlexperiments performed directly on the stainless steel plate. This isunder the assumption that on smooth stainless steel the slip length isnegligible. The torque results of these tests were set as a reference,from which we can calculate drag reduction on the slippery roughsurface.

The Peltier plate was maintained at a constant temperature of 23° C. inall the tests. To minimize measurement errors, the liquid meniscus atthe edge of the cone was well controlled by monitoring through a macrocamera maintain the constant liquid volume.

We systematically tested the lubricants with the viscosities from 72.2cP to 988 cP. Our results show that the drag reduction on slippery roughsurface is comparable to conventional superhydrophobic surfaces.

Sustainable drag reduction for marine ships requires not only dragreduction, but also anti-fouling and robust lubricant retention. Highlyviscous lubricant can significantly enhance the longevity. Combined withthe anti-fouling and robustness of the lubricant, such a slippery roughsurface can reduce drag for marine ships or heat exchangers.

Only the preferred embodiment of the present invention and examples ofits versatility are shown and described in the present disclosure. It isto be understood that the present invention is capable of use in variousother combinations and environments and is capable of changes ormodifications within the scope of the inventive concept as expressedherein. Thus, for example, those skilled in the art will recognize, orbe able to ascertain, using no more than routine experimentation,numerous equivalents to the specific substances, procedures andarrangements described herein. Such equivalents are considered to bewithin the scope of this invention, and are covered by the followingclaims.

1-10. (canceled)
 11. A method of preparing a slippery rough surface, themethod comprising: texturing a surface of a substrate with a pluralityof raised first elements and a plurality of second elements thereon; andapplying a lubricant layer over the plurality of raised first elementsand between the plurality of second elements.
 12. The method of claim11, further comprising silanizing the textured surface prior to applyingthe lubricant layer.
 13. The method of claim 11, wherein the surface ofthe substrate is a metal, plastic, ceramic, glass or combinationthereof.
 14. The method of claim 11, wherein the plurality of secondelements have an average height of between 0.01 μm and 10 μm.
 15. Themethod of claim 11, wherein the plurality of raised first elements havean average height of between 0.5 μm and 500 μm, and wherein theplurality of second elements have an average height of between 0.01 μmand 10 μm.
 16. The method of claim 12, wherein the surface of thesubstrate is a metal, plastic, ceramic, glass or combination thereof.17. The method of claim 12, wherein the plurality of second elementshave an average height of between 0.01 μm and 10 μm.
 18. The method ofclaim 13, wherein the plurality of second elements have an averageheight of between 0.01 μm and 10 μm.
 19. The method of claim 12, whereinthe plurality of raised first elements have an average height of between0.5 μm and 500 μm, and wherein the plurality of second elements have anaverage height of between 0.01 μm and 10 μm.
 20. The method of claim 13,wherein the plurality of raised first elements have an average height ofbetween 0.5 μm and 500 μm, and wherein the plurality of second elementshave an average height of between 0.01 μm and 10 μm.
 21. The method ofclaim 14, wherein the plurality of raised first elements have an averageheight of between 0.5 μm and 500 μm, and wherein the plurality of secondelements have an average height of between 0.01 μm and 10 μm.